Quantum Pathways Through Magnetic Breakdown

We establish a direct mapping between canonical quantum-optics models—the single-photon and two-photon quantum Rabi models—and magnetic-breakdown phenomena in minimal two-band condensed-matter systems. In these Hamiltonians, the problem of Bloch electrons in a magnetic field maps exactly onto Rabi models. The ultrastrong-coupling regime corresponds to field-induced tunneling between semiclassical orbits, which produces additional quantum-oscillation frequencies. Using an adiabatic approximation, we derive a closed-form expression for the high-field de Haas–van Alphen signal. We identify the superradiant transition of the Rabi models with Lifshitz transitions of the underlying two-band electronic structure. These results furnish a compact and experimentally testable theory of magnetic breakdown.